Grade: 7 Unit: 3 Week: 4 Dates: 12/3 – 12/7 Content: Apply Percents Theme Essential Question: How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions:
How do you apply the concept of percent to solve real-world and mathematical problems?
Standards:
7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.
Objectives: Review Concepts
The student will change decimals and fractions to percents and percents to decimal and fractions.
The student will change ratios to percents and percents to ratios.
The student will apply the concept of percent to real world situations such as finding simple interest, tax, commissions, fees, and percent of error to solve problems.
The student will determine the percent of increase and decrease of given problems.
The student will use mental math to calculate reasonableness of their answers to percent problems.
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team: Using the rate table concept or solving equation techniques, help students make the connection to the simplified strategy of cross-multiply and divide in solving ratio equal to ratio problems. Background Information Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Because percents have been introduced as rates in Grade 6, the work with percents should continue to follow the thinking involved with rates and proportions. Solutions to problems can be found by using the same strategies for solving rates, such as looking for equivalent ratios or based upon understandings of decimals. Previously, percents have focused on “out of 100”; now percents above 100 are encountered.
Providing opportunities to solve problems based within contexts that are relevant to 7th graders will connect meaning to rates, ratios and proportions. Examples include: researching newspaper ads and constructing their own question(s), keeping a log of prices (particularly sales) and determining savings by purchasing items on sale, timing students as they walk a lap on the track and figuring their rates, creating open-ended problem scenarios with and without numbers to give students the opportunity to demonstrate conceptual understanding, inviting students to create a similar problem to a given problem and explain their reasoning. Assessment: Product
Continue with the portfolio concept
Using the Frayer Model concept, adjust by changing the center from”Proportional Relationships” to “Percentage”
Simple Interest Activity:
The student has $__ to put into a saving account.
Create a table to determine simple interest give the rates of 0%, 2%, 4%, and 6% for one year, rate vs. interest
Develop of graph (rate, Interest)
Write an equation
AND/OR
Continue with the Family Trip from lesson 3-3; find the price for hotel accommodations for the three price ranges.
Given: A 15% discount for a three nights stay and
Sales tax on the rooms 8.25%
Key Questions
What does percent mean?
How do you write a percent as a decimal?
How do you find a percent of a number?
How can you use percents to solve problems?
How do you estimate a 15% tip without a calculator?
To find simple interest on an original amount, what two pieces of the information do you need?
What is meant by percent of increase/decrease?
Observable Student Behaviors
The student can apply the concept of percent to solve real-world and mathematical problems.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Houghton Mifflin On Core Mathematics Middle School Grade 7 Unit 2-4, p. 47-50
ABC Mastering the Common Core in Mathematics
Finding the percent of a total, Chapter 5.4, p. 46
Percent of Increase or Decreased, Chapter 5.5, p. 47-48
Tips and Commissions, Chapter 5.6, p. 49
Finding the Amount of Discount, Chapter 5.7, p.50
Finding the Discounted Sale Price, Chapter 5.8, p. 51
Markups, Chapter 5.9, p. 52
Sales Tax, Chapter 5.10, p. 53
Understanding Simple Interest, Chapter 5.11, p. 54
Percent Error, Chapter 5.12, p. 55
Review and Test, p. 56-59
Gizmo Correlation
7.RP.3
Estimating Population Size
Adjust the number of fish in a lake to be tagged and the number of fish to be recaptured. Use the number of tagged fish in the catch to estimate the number of fish in the lake.
Percent of Change
Apply markups and discounts using interactive "percent rulers." Improve number sense for percents with this dynamic, visual tool. Reinforce the original cost (or original price) as the baseline for percent calculations.
Percents and Proportions
Find a part from the percent and whole, a percent from the part and whole, or a whole from the part and percent using a graphic model.
Beanstalk: The Measure of A Giant (A Math Adventure) Ann McCallum This fractured fairy tale tries to squeeze in a math lesson about ratios, but it isn’t successful. Jack wakes up to discover a beanstalk outside his window, climbs up, and befriends a lonely giant boy at the top. The two go off to play but quickly realize that the difference in their size is going to make most games difficult. Trying to play hoop ball, for example, proves to be impossible until Jack realizes that I need a hoop that as high for me as your hoop is for you. A few measurements later, the boys realize that Rays hoop is three times his height, so they figure out how tall Jacks should be, and fashion one for him. Once home, Jack decides to make a checker set for Ray and figures out what size to make it. The story ends with the two friends eating lunch outside with Jacks mother, who wishes for a word to describe the relationship between the sizes of two things, since the boys dealt with their differences so wonderfully. Jack decides that they should call it a Ray show, since Ray showed Jack that their things were the perfect size for each of them. The author sums the story up by explaining that today it is spelled ratio.
Mathematics in Children's Literature: Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
The teaching Channel currently offers videos of K-12 mathematics teaching aligned with the Common Core Sate Standards, which would be perfect for professional development with teacher teams.
Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
Grade: 7 Unit: 3 Week: 4 Dates: 12/3 – 12/7
Content: Apply Percents
Theme Essential Question:
How can you analyze proportional relationships and use them to solve real-world and mathematical problems?
Essential Questions:
Standards:
Objectives:
Review Concepts
Reflections and/or Comments from your PCSSD 7th Grade Curriculum Team:
Using the rate table concept or solving equation techniques, help students make the connection to the simplified strategy of cross-multiply and divide in solving ratio equal to ratio problems.
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials at http://www.azed.gov/educator-certification/
Because percents have been introduced as rates in Grade 6, the work with percents should continue to follow the thinking involved with rates and proportions. Solutions to problems can be found by using the same strategies for solving rates, such as looking for equivalent ratios or based upon understandings of decimals. Previously, percents have focused on “out of 100”; now percents above 100 are encountered.
Providing opportunities to solve problems based within contexts that are relevant to 7th graders will connect meaning to rates, ratios and proportions. Examples include: researching newspaper ads and constructing their own question(s), keeping a log of prices (particularly sales) and determining savings by purchasing items on sale, timing students as they walk a lap on the track and figuring their rates, creating open-ended problem scenarios with and without numbers to give students the opportunity to demonstrate conceptual understanding, inviting students to create a similar problem to a given problem and explain their reasoning.
Assessment:
Product
Key Questions
Observable Student Behaviors
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
percent increase/decrease simple interest tax
commission fees
- Highly Recommended
http://illustrativemathematics.org/illustrations/148 (7.PR.3)http://illustrativemathematics.org/illustrations/130 (7.PR.3)
http://illustrativemathematics.org/illustrations/121 (7.PR.3)
http://illustrativemathematics.org/illustrations/117 (7.PR.3)
http://illustrativemathematics.org/illustrations/102 (7.PR.3)
http://illustrativemathematics.org/illustrations/105 (7.PR.3)
http://illustrativemathematics.org/illustrations/106 (7.PR.3)
http://illustrativemathematics.org/illustrations/266 (7.PR.3)
The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Diverse Learners
Homework: (Teacher Discretion)
Terminology for Teachers:
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources:
Professional Texts:
Literary Texts
- Ratios
http://sci.tamucc.edu/~eyoung/ratio_prop_literature.html- Beanstalk: The Measure of A Giant (A Math Adventure) Ann McCallum This fractured fairy tale tries to squeeze in a math lesson about ratios, but it isn’t successful. Jack wakes up to discover a beanstalk outside his window, climbs up, and befriends a lonely giant boy at the top. The two go off to play but quickly realize that the difference in their size is going to make most games difficult. Trying to play hoop ball, for example, proves to be impossible until Jack realizes that I need a hoop that as high for me as your hoop is for you. A few measurements later, the boys realize that Rays hoop is three times his height, so they figure out how tall Jacks should be, and fashion one for him. Once home, Jack decides to make a checker set for Ray and figures out what size to make it. The story ends with the two friends eating lunch outside with Jacks mother, who wishes for a word to describe the relationship between the sizes of two things, since the boys dealt with their differences so wonderfully. Jack decides that they should call it a Ray show, since Ray showed Jack that their things were the perfect size for each of them. The author sums the story up by explaining that today it is spelled ratio.
- Mathematics in Children's Literature:
Click on the following link, http://libguides.nl.edu/mathinchildrenslit, and then look under Math and Literature Bibliographies.Many children's books include math concepts and can be used to help teach them in a fun way. This website includes several annotated Lists of Children's Literature including the math concepts and grade levels.
- Middle & High School: Literature in Mathematics
Many books include websites with lesson ideas.http://sci.tamucc.edu/~eyoung/middle_school_literature.html
- Lesson Plans for Using Literature in Middle and High School Mathematics (developed by Leonor and edited by Elaine)
http://sci.tamucc.edu/~eyoung/Literature%20webpages/Leonor/index.html- Miscellaneous Math and Children's Literature
http://sci.tamucc.edu/~eyoung/literature.htmlInformational Texts
Art, Music, and Media
Manipulatives
Games
- Per Cent Problems:
http://www.mathplayground.com/mathatthemall1.htmlhttps://www.teachingchannel.org/videos/junior-high-math-lesson
SMART Board Notebook file for Proportions Trail (Notebook
Videos
SMART Board Lessons, Promethean Lessons
Other Activities, etc.
- http://www.mathgoodies.com/lessons/vol5/division.html
- Interactivate is a set of free, online courseware for exploration in science and mathematics. It is comprised of activities, lessons, and discussions. The site is structured around collections of activities, lessons, and discussions.
http://www.shodor.org/interactivate/guide/Language
Arts
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
7 Matrix
Accelerated 7
Matrix
Week 1
Week 2
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6